David Cameron was doing his best on Sunday to laugh off the antics of Boris Johnson, who showed the Tory party last week that he remained an ever-present threat to the prime minister.

On the eve of the London mayor's whirlwind appearance at the Tory conference, Cameron spoke of how relaxed he was to have "the blond-haired mop sounding off from time to time".

Downing Street is officially unbothered by Johnson, who has taken to firing potshots at the prime minister on a weekly basis. Days after the mayor and his family enjoyed a jolly day out to Chequers last Sunday, Johnson accused Cameron of risking an "economic catastrophe" over aviation policy.

Johnson will sweep into the conference on Monday for two speeches in the space of 24 hours. He will speak from the official platform on Tuesday, but will probably have most fun on Monday when he addresses a rally organised by ConservativeHome, titled "Boris Johnson 2012: Re-elected and Olympotastic".

The title is designed to irritate Downing Street on two levels. Firstly, it shows that Johnson won re-election, after Cameron failed to win an overall Commons majority in 2010. Secondly, it reminds everyone of his latest triumph, upstaging the prime minister at the parade for the Olympics and Paralympics.

Cameron told the Sunday Telegraph: "I am, relatively, as you can see, relaxed about having the blond-haired mop sounding off from time to time. Every premiership has its backdrop, and I suspect this is just going to be one of mine."

Michael Fallon, the business minister, highlighted No 10's real thinking when he told the FT on Saturday that he hoped Johnson enjoyed his "day in the sun". The emphasis was on a day, rather than days.

One minister said Johnson was perfecting the art of attracting attention but did not pose a serious threat. "Local government has its place," the minister said of Britain's most senior municipal political figure. "Boris is of course a blond bombshell. But he is not like that other famous blond bombshell, Michael Heseltine. This really does not feel like a Heseltine moment."

Heseltine resigned as defence secretary in 1986 in a row over whether Westland Helicopters should tie up with a European or a US firm. He then embarked on a four-year campaign to rally the Tory grassroots to his vision of a One Nation party. In 1990 he overthrew, but failed to replace, Margaret Thatcher.